Why is sodium-intercalated graphite unstable?

Na-ion batteries offer an attractive low-cost alternative to Li-ion batteries. Although graphite is used as the negative electrode in conventional Li-ion batteries, attempts to use it in Na-ion batteries have been hampered by the inability of Na to form graphite intercalation compounds (GICs) under moderate conditions. It is generally considered that this is due to the size mismatch between Na and the graphite interlayer spacings, but here we show with detailed first-principles calculations of Li, Na, K, Rb, and Cs GICs that the major reason is the change in chemical bonding between alkali metal (AM) ion and C atoms. van der Waals correction terms are introduced to better reproduce the layered graphite structure, and calculated formation energies of GICs AMC(6), where AM = Li, Na, K, Rb, and Cs, are found to become less negative (less stable) as ion size decreases from Cs to Na as a result of weakening ionic bonding, until the formation energy of NaC6 becomes positive. The much smaller Li ion represents an exception to this trend, as its bonds with C atoms contain a covalent component, resulting in a negative formation energy. These subtle differences in staging for the different alkali metals explain why graphite is a good intercalation material for Li and K but not for Na.